I would suspect that both the hot and cold lines had the additional tee taps to make supplies for a Dishwasher off the hot side and perhaps a refrigerator ice maker on the cold side. We are about to eliminate that mess.
You stated that you intend to connect a dishwasher and no doubt you also have an icemaker so we should make provisions for those two items, which we can do by installing the side outlet (double port)angle stop valves as you suggested.
Both a dishwasher and an icemaker have electrically operated solenoid valves, which are classified as fast acting valves, to control their water supply. The codes now require that we install water hammer arrestors in the near proximity of all "Fast Acting Valves" so we will retain the water hammer arrestors.
To transition from copper to CPVC you would need to first install a Copper x CPVC union or a Female copper thread adapter and use a CPVC male thread adapter to connect the CPVC. The code prohibits using compression fittings in concealed locations so whichever material you choose you will still need to make at least one solder joint on each of the hot and cold water lines, but not to worry, i have a game plan that should make that very easy for you.
Before you begin, turn the house "Main Water Supply Valve" or a zone valve off to stop the water supply to these lines. Place a container under the angle stop valves and open the valves to drain the water out of the pipes.
Fortunately the water supply is coming down from overhead, so once the main water valve is turned off and the lines drained you can cut the lines without making a mess and the vertical drop will clear so you will not have the problem of standing water in the line that would make soldering difficult.
I would then prefab the stubout, water hammer arrestor and a short vertical stub up to the point were you intend to connect to the water lines on a bench were it is easy to do. Prefab one for both the hot and cold water lines, then all you will need to do is make one solder joint on each line under the sink.
The copper lines coming down are quite long and not well supported so you should be able to carefully spring them out away from the wall while soldering. There appears to be ample insulation in the wall so the risk of fire is greatly diminished, but just to be safe you can quickly make a heat shield for the soldering process. Take an empty 3lb coffee can and cut both ends out, then split it down one side and open it up so it can be slipped behind the joint to prevent the torch flame from hitting the insulation or studding while soldering.
Thoroughly clean the end of the stub up on your prefab section and the end of the water line where you cut it, then apply flux with a flux brush. Connect both lines together with a copper coupling and solder it in place.
NOTE: Do Not install the angle stop valves until after you make the final solder connection. By leaving the end of the pipe open it will provide a vent in case there is an residual water in the line that could cause steam pressure.
When soldering begin by applying heat to both the pipes and the coupling to preheat, then apply the tip of the torch flame to the coupling only as you apply the solder. The moment the solder begins to flow you should be able to pull the torch flame back and continue feeding solder until you have a good fill of solder completely around the fitting. Use a wet rag to wipe the excess solder and flux off the joint, then do the second line and your done.
The stub outs for the angle stop valves will be outside the finish wall in an exposed location so you may use the compression type angle stop valves. I would suggest using the compression type angle stops so if your configuration changes in future and you no longer need the dual port type valves you can change the valves without soldering.
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